Analytical Estimates of Gravitational Wave Background Anisotropies from Shot Noise and Large-Scale Structure in Pulsar Timing Arrays

TL;DR

This paper predicts gravitational wave background anisotropies from supermassive black hole binaries, highlighting shot noise as a detectable signal in pulsar timing array data and contrasting it with the smaller large-scale structure effects.

Contribution

It provides empirically calibrated models for GWB anisotropies, emphasizing the frequency dependence of shot noise and its detectability with current and future PTA observations.

Findings

Shot-noise anisotropies are near current detection limits.

Frequency dependence tests SMBHB residence times.

LSS anisotropies are significantly smaller and harder to detect.

Abstract

An important next step for pulsar timing arrays (PTAs) is to measure anisotropies in the gravitational wave background (GWB) at $\sim$ nano-Hz frequencies. We calculate the expected GWB anisotropies using empirically calibrated models for the merger rates of supermassive black hole binaries (SMBHBs). The anisotropies reflect both shot-noise in the discrete SMBHB populations while also tracing, in part, the large-scale structure (LSS) of the universe. The shot-noise term is sensitive to the high-mass end of the merging SMBH mass function, depends somewhat on the low-redshift tail of the merger distribution, and is a strong function of observing frequency. The precise frequency dependence provides a test of SMBHB residence times. In our models, the mean shot-noise anisotropy typically lies close to or above the broad frequency-band NANOGrav upper limits. Consequently, near-future PTA data, and potentially re-analyses of existing measurements using frequency-dependent shot-noise anisotropy templates, should be capable of detecting this signal or placing meaningful constraints on SMBHB merger models. A full interpretation, however, will require modeling the probability distribution of shot-noise amplitudes rather than relying solely on ensemble-averaged predictions. The LSS-induced anisotropies are at least two to three orders of magnitude smaller. Although the LSS contribution contains valuable information regarding the redshift distribution and clustering bias of the merging SMBHBs, detecting this component will be challenging.